Questions: Question 25 The FBI has been collecting fingerprint cards since 1924. Their collection has grown to over 200 million cards. When digitized, each fingerprint card turns into about 10 MB of data (A megabyte [MB] is 2^20 ≈ one million bytes). a. How many bytes of storage will they need? They will need bytes. b. A compression routine called the WSQ method will compress the bytes by ratio 12.9 to 1. Approximately how many bytes of storage will the FBI need for the compressed data? They will need bytes for the compressed data.

Solution Steps

To solve these questions, we need to perform the following steps:

a. Calculate the total storage required in bytes by multiplying the number of fingerprint cards by the size of each card in bytes. b. Calculate the storage required after compression by dividing the total storage by the compression ratio.

Given:

• Number of fingerprint cards: \(200,000,000\)
• Size of each card: \(10 \, \text{MB}\)

First, convert the size of each card to bytes: \[ 10 \, \text{MB} = 10 \times 2^{20} \, \text{bytes} = 10 \times 1,048,576 \, \text{bytes} = 10,485,760 \, \text{bytes} \]

Next, calculate the total storage required: \[ \text{Total storage} = 200,000,000 \times 10,485,760 \, \text{bytes} = 2,097,152,000,000,000 \, \text{bytes} \]

Given:

• Compression ratio: \(12.9\)

Calculate the storage required after compression: \[ \text{Compressed storage} = \frac{2,097,152,000,000,000 \, \text{bytes}}{12.9} \approx 162,569,922,480,620.16 \, \text{bytes} \]

Final Answer